Cremona's table of elliptic curves

27072 = 2⁶ · 3² · 47

Class	r	Atkin-Lehner	Eigenvalues
27072a (1 curve)	1	2+ 3+ 47+	2+ 3+  1 -1  1 -4  6 -2
Curve Equation t Generators 27072a1 [0,0,0,-162,702] 1 [21:81:1]
27072b (1 curve)	1	2+ 3+ 47+	2+ 3+ -1  1  1 -4 -6  2
Curve Equation t Generators 27072b1 [0,0,0,-18,26] 1 [1:3:1]
27072c (1 curve)	1	2+ 3+ 47+	2+ 3+  3  1 -3  0  0  4
Curve Equation t Generators 27072c1 [0,0,0,-36,82] 1 [3:1:1]
27072d (1 curve)	1	2+ 3+ 47+	2+ 3+ -3  3  1  4  4 -4
Curve Equation t Generators 27072d1 [0,0,0,-864,-7776] 1 [-126:351:8]
27072e (1 curve)	0	2+ 3+ 47-	2+ 3+  1  1 -1 -4  6  2
Curve Equation t 27072e1 [0,0,0,-162,-702] 1
27072f (1 curve)	2	2+ 3+ 47-	2+ 3+ -1 -1 -1 -4 -6 -2
Curve Equation t Generators 27072f1 [0,0,0,-18,-26] 1 [-3:1:1]&[5:3:1]
27072g (1 curve)	0	2+ 3+ 47-	2+ 3+  3  3 -1  4 -4 -4
Curve Equation t 27072g1 [0,0,0,-96,288] 1
27072h (1 curve)	0	2+ 3+ 47-	2+ 3+ -3  1  3  0  0  4
Curve Equation t 27072h1 [0,0,0,-324,-2214] 1
27072i (2 curves)	0	2+ 3- 47+	2+ 3-  0  0  0  2 -2 -6
Curve Equation t 27072i1 [0,0,0,-2775,-55748] 2 27072i2 [0,0,0,-660,-138656] 2
27072j (2 curves)	0	2+ 3- 47+	2+ 3-  0  4  0 -6  6 -2
Curve Equation t 27072j1 [0,0,0,-4620,172528] 2 27072j2 [0,0,0,-82380,9099376] 2
27072k (1 curve)	0	2+ 3- 47+	2+ 3- -1 -1 -1  4  4  6
Curve Equation t 27072k1 [0,0,0,-2928,-58336] 1
27072l (1 curve)	0	2+ 3- 47+	2+ 3- -1 -1  3  2  6  6
Curve Equation t 27072l1 [0,0,0,-7968,273184] 1
27072m (1 curve)	0	2+ 3- 47+	2+ 3- -1 -1  3 -2  0  0
Curve Equation t 27072m1 [0,0,0,-6258,167974] 1
27072n (2 curves)	0	2+ 3- 47+	2+ 3-  2  0 -6  0  6  4
Curve Equation t 27072n1 [0,0,0,276,-6608] 2 27072n2 [0,0,0,-4044,-91280] 2
27072o (2 curves)	0	2+ 3- 47+	2+ 3-  2  4 -2 -4  6  8
Curve Equation t 27072o1 [0,0,0,-84,15392] 2 27072o2 [0,0,0,-9804,369200] 2
27072p (2 curves)	0	2+ 3- 47+	2+ 3- -2  0 -2 -4 -2 -8
Curve Equation t 27072p1 [0,0,0,-15760236,-30663640784] 2 27072p2 [0,0,0,-270851916,-1715595205520] 2
27072q (1 curve)	0	2+ 3- 47+	2+ 3-  3  3  3  2  4  0
Curve Equation t 27072q1 [0,0,0,-426,3382] 1
27072r (1 curve)	0	2+ 3- 47+	2+ 3-  3 -5  3  6 -2  2
Curve Equation t 27072r1 [0,0,0,-336,1312] 1
27072s (1 curve)	0	2+ 3- 47+	2+ 3- -3  1 -1  2 -4  4
Curve Equation t 27072s1 [0,0,0,-87474,-6707374] 1
27072t (1 curve)	2	2+ 3- 47+	2+ 3- -3 -3 -5 -2  6  6
Curve Equation t Generators 27072t1 [0,0,0,-444,-1366] 1 [43:-243:1]&[-5:27:1]
27072u (2 curves)	0	2+ 3- 47+	2+ 3- -4 -4  0  2  6 -6
Curve Equation t 27072u1 [0,0,0,-8652,-379280] 2 27072u2 [0,0,0,-146892,-21668240] 2
27072v (2 curves)	1	2+ 3- 47-	2+ 3-  0  0  0  2 -2  6
Curve Equation t Generators 27072v1 [0,0,0,-2775,55748] 2 [352:6534:1] 27072v2 [0,0,0,-660,138656] 2 [-50:216:1]
27072w (2 curves)	1	2+ 3- 47-	2+ 3-  0  0  2  4  2  2
Curve Equation t Generators 27072w1 [0,0,0,180,9072] 2 [-12:72:1] 27072w2 [0,0,0,-5580,154224] 2 [180:2232:1]
27072x (2 curves)	1	2+ 3- 47-	2+ 3-  0 -4 -4 -2 -2  2
Curve Equation t Generators 27072x1 [0,0,0,420,848] 2 [16:108:1] 27072x2 [0,0,0,-1740,6896] 2 [-43:47:1]
27072y (1 curve)	1	2+ 3- 47-	2+ 3-  1  3  1  2 -2 -2
Curve Equation t Generators 27072y1 [0,0,0,-35472,2432032] 1 [-199:1269:1]
27072z (1 curve)	1	2+ 3- 47-	2+ 3- -1  1 -3 -2  0  0
Curve Equation t Generators 27072z1 [0,0,0,-6258,-167974] 1 [-2300:6561:64]
27072ba (1 curve)	1	2+ 3- 47-	2+ 3- -1 -3  1  2 -2 -6
Curve Equation t Generators 27072ba1 [0,0,0,-948,11234] 1 [19:9:1]
27072bb (1 curve)	1	2+ 3- 47-	2+ 3- -1 -3 -3  4 -8  6
Curve Equation t Generators 27072bb1 [0,0,0,-48,34] 1 [-1:9:1]
27072bc (4 curves)	1	2+ 3- 47-	2+ 3-  2  0  0 -2 -2  0
Curve Equation t Generators 27072bc1 [0,0,0,33396,1174768] 2 [3716:226800:1] 27072bc2 [0,0,0,-150924,9948400] 4 [670236:-50864575:21952] 27072bc3 [0,0,0,-1233804,-520662800] 2 [-5528559231300:-22202179748825:8539701184] 27072bc4 [0,0,0,-2017164,1102072048] 2 [2082:195097:8]
27072bd (4 curves)	1	2+ 3- 47-	2+ 3-  2  0  4  2 -2  0
Curve Equation t Generators 27072bd1 [0,0,0,-1164,-43792] 2 [2446:120960:1] 27072bd2 [0,0,0,-27084,-1713040] 4 [-106345646:-35199360:1092727] 27072bd3 [0,0,0,-35724,-527632] 2 [-1617:31913:27] 27072bd4 [0,0,0,-433164,-109730320] 2 [-30763006447530:-42252851285:80957957976]
27072be (2 curves)	1	2+ 3- 47-	2+ 3-  2 -4  2 -4  6 -8
Curve Equation t Generators 27072be1 [0,0,0,-84,-15392] 2 [29:81:1] 27072be2 [0,0,0,-9804,-369200] 2 [677:17415:1]
27072bf (1 curve)	1	2+ 3- 47-	2+ 3-  3 -3 -3  2  4  0
Curve Equation t Generators 27072bf1 [0,0,0,-426,-3382] 1 [-94:9:8]
27072bg (1 curve)	1	2+ 3- 47-	2+ 3- -3 -1  1  2 -4 -4
Curve Equation t Generators 27072bg1 [0,0,0,-87474,6707374] 1 [21:2209:1]
27072bh (2 curves)	1	2+ 3- 47-	2+ 3- -3 -1 -3  4  0 -2
Curve Equation t Generators 27072bh1 [0,0,0,-1344,-18016] 1 [-23:27:1] 27072bh2 [0,0,0,-18624,973856] 1 [49:-423:1]
27072bi (1 curve)	1	2+ 3- 47-	2+ 3- -3 -1  5  4  4  2
Curve Equation t Generators 27072bi1 [0,0,0,-164784,-25742176] 1 [-519155:94041:2197]
27072bj (1 curve)	0	2- 3+ 47+	2- 3+  1  3 -3  0 -2 -6
Curve Equation t 27072bj1 [0,0,0,-222,-1098] 1
27072bk (1 curve)	0	2- 3+ 47+	2- 3+ -1 -3 -3  0  2  6
Curve Equation t 27072bk1 [0,0,0,-1998,-29646] 1
27072bl (2 curves)	0	2- 3+ 47+	2- 3+  2 -4  4 -6  0 -2
Curve Equation t 27072bl1 [0,0,0,-459,2808] 2 27072bl2 [0,0,0,-6804,216000] 2
27072bm (2 curves)	0	2- 3+ 47+	2- 3+ -2  4  4 -6  0  2
Curve Equation t 27072bm1 [0,0,0,-51,104] 2 27072bm2 [0,0,0,-756,8000] 2
27072bn (1 curve)	0	2- 3+ 47+	2- 3+  3 -3  1  4 -4  4
Curve Equation t 27072bn1 [0,0,0,-96,-288] 1
27072bo (1 curve)	2	2- 3+ 47+	2- 3+ -3 -1 -3  0  0 -4
Curve Equation t Generators 27072bo1 [0,0,0,-324,2214] 1 [15:27:1]&[7:17:1]
27072bp (1 curve)	1	2- 3+ 47-	2- 3+  1 -3  3  0 -2  6
Curve Equation t Generators 27072bp1 [0,0,0,-222,1098] 1 [-11:47:1]
27072bq (1 curve)	1	2- 3+ 47-	2- 3+ -1  3  3  0  2 -6
Curve Equation t Generators 27072bq1 [0,0,0,-1998,29646] 1 [18:1269:8]
27072br (2 curves)	1	2- 3+ 47-	2- 3+  2  4 -4 -6  0  2
Curve Equation t Generators 27072br1 [0,0,0,-459,-2808] 2 [-16068:27594:2197] 27072br2 [0,0,0,-6804,-216000] 2 [-288401386:22274855:6028568]
27072bs (2 curves)	1	2- 3+ 47-	2- 3+ -2 -4 -4 -6  0 -2
Curve Equation t Generators 27072bs1 [0,0,0,-51,-104] 2 [-4:6:1] 27072bs2 [0,0,0,-756,-8000] 2 [32:24:1]
27072bt (1 curve)	1	2- 3+ 47-	2- 3+  3 -1  3  0  0 -4
Curve Equation t Generators 27072bt1 [0,0,0,-36,-82] 1 [7:3:1]
27072bu (1 curve)	1	2- 3+ 47-	2- 3+ -3 -3 -1  4  4  4
Curve Equation t Generators 27072bu1 [0,0,0,-864,7776] 1 [9:27:1]
27072bv (2 curves)	1	2- 3- 47+	2- 3-  0  0  2  4  2  2
Curve Equation t Generators 27072bv1 [0,0,0,-156900,24211712] 2 [268:1188:1] 27072bv2 [0,0,0,-2518860,1538700464] 2 [7671:785323:27]
27072bw (2 curves)	1	2- 3- 47+	2- 3-  0  0 -2  4  2 -2
Curve Equation t Generators 27072bw1 [0,0,0,180,-9072] 2 [21:63:1] 27072bw2 [0,0,0,-5580,-154224] 2 [405:8001:1]
27072bx (2 curves)	1	2- 3- 47+	2- 3-  0  4  4 -2 -2 -2
Curve Equation t Generators 27072bx1 [0,0,0,420,-848] 2 [18:112:1] 27072bx2 [0,0,0,-1740,-6896] 2 [-22:144:1]
27072by (1 curve)	1	2- 3- 47+	2- 3-  1  1 -5  6  0 -4
Curve Equation t Generators 27072by1 [0,0,0,-102,-142] 1 [13:27:1]
27072bz (1 curve)	1	2- 3- 47+	2- 3-  1 -3 -1  2 -2  2
Curve Equation t Generators 27072bz1 [0,0,0,-35472,-2432032] 1 [-958:2511:8]
27072ca (1 curve)	1	2- 3- 47+	2- 3- -1  3 -1  2 -2  6
Curve Equation t Generators 27072ca1 [0,0,0,-948,-11234] 1 [-483:1:27]
27072cb (1 curve)	1	2- 3- 47+	2- 3- -1  3 -1 -2  0  0
Curve Equation t Generators 27072cb1 [0,0,0,-3918,-94394] 1 [-48125:279:1331]
27072cc (1 curve)	1	2- 3- 47+	2- 3- -1  3  3  4 -8 -6
Curve Equation t Generators 27072cc1 [0,0,0,-48,-34] 1 [-5:9:1]
27072cd (4 curves)	1	2- 3- 47+	2- 3-  2  0  0 -2 -2  0
Curve Equation t Generators 27072cd1 [0,0,0,33396,-1174768] 2 [4141:266733:1] 27072cd2 [0,0,0,-150924,-9948400] 4 [-70844000:-1445352460:704969] 27072cd3 [0,0,0,-1233804,520662800] 2 [112730:1486656:125] 27072cd4 [0,0,0,-2017164,-1102072048] 2 [-1701826336672410208:1651904642313392020:2074476842443153]
27072ce (4 curves)	1	2- 3- 47+	2- 3-  2  0 -4  2 -2  0
Curve Equation t Generators 27072ce1 [0,0,0,-1164,43792] 2 [-19:243:1] 27072ce2 [0,0,0,-27084,1713040] 4 [173:1485:1] 27072ce3 [0,0,0,-35724,527632] 2 [-46:1440:1] 27072ce4 [0,0,0,-433164,109730320] 2 [528055:758295:1331]
27072cf (2 curves)	1	2- 3- 47+	2- 3- -3  1  3  4  0  2
Curve Equation t Generators 27072cf1 [0,0,0,-1344,18016] 1 [17:9:1] 27072cf2 [0,0,0,-18624,-973856] 1 [-9395:4581:125]
27072cg (1 curve)	1	2- 3- 47+	2- 3- -3  1 -5  4  4 -2
Curve Equation t Generators 27072cg1 [0,0,0,-164784,25742176] 1 [209:657:1]
27072ch (2 curves)	1	2- 3- 47+	2- 3- -4  0  2  4 -6  6
Curve Equation t Generators 27072ch1 [0,0,0,348,4480] 2 [2:72:1] 27072ch2 [0,0,0,-2892,49840] 2 [-27:329:1]
27072ci (2 curves)	0	2- 3- 47-	2- 3-  0  0 -2  4  2 -2
Curve Equation t 27072ci1 [0,0,0,-156900,-24211712] 2 27072ci2 [0,0,0,-2518860,-1538700464] 2
27072cj (2 curves)	0	2- 3- 47-	2- 3-  0 -4  0 -6  6  2
Curve Equation t 27072cj1 [0,0,0,-4620,-172528] 2 27072cj2 [0,0,0,-82380,-9099376] 2
27072ck (1 curve)	0	2- 3- 47-	2- 3-  1 -1  5  6  0  4
Curve Equation t 27072ck1 [0,0,0,-102,142] 1
27072cl (1 curve)	0	2- 3- 47-	2- 3- -1  1  1  4  4 -6
Curve Equation t 27072cl1 [0,0,0,-2928,58336] 1
27072cm (1 curve)	0	2- 3- 47-	2- 3- -1  1 -3  2  6 -6
Curve Equation t 27072cm1 [0,0,0,-7968,-273184] 1
27072cn (1 curve)	2	2- 3- 47-	2- 3- -1 -3  1 -2  0  0
Curve Equation t Generators 27072cn1 [0,0,0,-3918,94394] 1 [-11:369:1]&[37:9:1]
27072co (2 curves)	0	2- 3- 47-	2- 3-  2  0  6  0  6 -4
Curve Equation t 27072co1 [0,0,0,276,6608] 2 27072co2 [0,0,0,-4044,91280] 2
27072cp (2 curves)	0	2- 3- 47-	2- 3- -2  0  2 -4 -2  8
Curve Equation t 27072cp1 [0,0,0,-15760236,30663640784] 2 27072cp2 [0,0,0,-270851916,1715595205520] 2
27072cq (1 curve)	0	2- 3- 47-	2- 3-  3  5 -3  6 -2 -2
Curve Equation t 27072cq1 [0,0,0,-336,-1312] 1
27072cr (1 curve)	0	2- 3- 47-	2- 3- -3  3  5 -2  6 -6
Curve Equation t 27072cr1 [0,0,0,-444,1366] 1
27072cs (2 curves)	2	2- 3- 47-	2- 3- -4  0 -2  4 -6 -6
Curve Equation t Generators 27072cs1 [0,0,0,348,-4480] 2 [14:56:1]&[16:72:1] 27072cs2 [0,0,0,-2892,-49840] 2 [-38:72:1]&[-22:56:1]
27072ct (2 curves)	0	2- 3- 47-	2- 3- -4  4  0  2  6  6
Curve Equation t 27072ct1 [0,0,0,-8652,379280] 2 27072ct2 [0,0,0,-146892,21668240] 2

Data from Elliptic Curve Data by J. E. Cremona.
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